Our group has developed a quantitative tool called momentum balance, which uses two-electron density matrices, to understand correlated electron motion in ground and excited states (Todd & Hollett, 2021) of atoms and molecules. The momentum balance is a measure of correlated electron motion as the difference between probability that electrons have the same or opposite momentum. Highly accurate wavefunctions and their two-electron density matrices of varying spin multiplicity of atoms and molecules are calculated using the extrapolated Full Configuration Interaction approach within the Quantum Package 2.0 software. The two-electron density matrix is obtained from the wavefunctions and analyzed using in-house software, including calculating momentum balance, momentum balance density, and two-electron density. Our group has precisely obtained the correlated electron motion of the ground state of atoms using the proposed methods (Todd & Hollett, 2021). We also found impressive results for the excited states of \(H_{2}\) molecule using the proposed methods. For instance, momentum balance can be used to describe the double wells in the potential energy curves of \(H_{2}\) molecule (Figure 1) obtained at various electronic excited states (Wang et al, 2006; Nakashima & Nakatsuji, 2018). Momentum balance can also be used to assess how the relative spin (opposite or parallel) of electrons in atoms influences their relative motion, and how this motion changes in the excited states. This study will advance our understanding of correlated electron motion to develop better electronic structure models of the ground and excited states, efficient tools for chemistry and materials research.

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